3D software like GeoGebra

GeoGebra 5.0 (with 3D) has been released:

https://www.geogebra.org/

There will be a public preview of GeoGebra 3D soon. Keep an eye on the GeoGebra forums :)

Geomview is fairly flexible, and allows you to work in Euclidean, spherical or hyperbolic geometry. Depending on which operating system you use it might be easier or harder to get it installed. It made it into the Ubuntu repositories recently, so if you're running Ubuntu it takes little effort to install.

That said, it's not the easiest software to use -- quite a ways away from the interface of GeoGebra. More often than not, if I need a high-quality rendered image of something 3-dimensional, I code a PovRay script and render it.

Blender is open-source and interactive. It appears to be quite flexible -- it's used to produce models for 3d video games, for example. I haven't really got comfortable using it, though.